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Professor of Mathematical Analysis. Two years later he was
promoted (at the age of twenty-seven) to the University of
Paris where, in 1886, he was again promoted, taking charge of
the course in mechanics and experimental physics (the last
seems rather strange, hi view of Poincare's exploits as a student
in the laboratory). Except for trips to scientific congresses in
Europe and a visit to the United States hi 1904 as an invited
lecturer at the St Louis Exposition, Poincare spent the rest of
Ms life in Paris as the ruler of French mathematics.
Poincare's creative period opened with the thesis of 1878 and
closed with his death in 1912 - when he was at the apex of his
powers. Into this comparatively brief span of thirty-four years
he crowded a mass of work that is sheerly incredible when we
consider the difficulty of most of it. His record is nearly 500
papers on new mathematics, many of them extensive memoirs,
and more than thirty books covering practically all branches of
mathematical physics, theoretical physics, and theoretical
astronomy as they existed in his day. This leaves out of account
his classics on the philosophy of science and his popular essays.
To give an adequate idea of this immense labour one would
have to be a second Polncare1, so we shall presently select two
or three of his most celebrated works for brief description,
apologizing here once for all for the necessary inadequacy.
Poineare's first successes were in the theory of differential
equations, to which he applied all the resources of the analysis
of which he was absolute master. This early choice for a major
effort already indicates Poincare's leaning toward the applica-
tions of mathematics, for differential equations have attracted
swarms of workers since the time of Newton chiefly because
they are of great importance in the exploration of the physical
universe. 'Pure* mathematicians sometimes like to imagine that
all their activities are dictated by their own tastes and that the
applications of science suggest nothing of interest to them.
Nevertheless some of the purest of the pure drudge away their
Jives over differential equations that first appeared in the
translation of physical situations into mathematical symbolism,
and it is precisely these practically suggested equations which
are the heart of the theory. A particular equation suggested by